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lisabon 2012 [21]
4 years ago
15

Drawing a card- four cards are drawn from a desk without replacement.Find these probabilities.

Mathematics
1 answer:
svetlana [45]4 years ago
5 0

The deck consists of 4 jacks, 26 black cards, and 13 hearts.

There is only 1 way of drawing all 4 jacks: \dbinom44=\dfrac{4!}{4!(4-4)!}=1.

There are \dbinom{26}4=14,950 ways of drawing 4 black cards.

There are \dbinom{13}4=715 ways of drawing 4 hearts.

There are \dbinom{52}4=270,725 ways of drawing any 4 cards.

The probabilities are then

a.

\dfrac{\binom44}{\binom{52}4}=\dfrac1{207,725}\approx0.00000369

b.

\dfrac{\binom{26}4}{\binom{52}4}=\dfrac{46}{833}\approx0.0552

c.

\dfrac{\binom{13}4}{\binom{52}4}=\dfrac{11}{4165}\approx0.00264

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